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Oblate nuclear shapes and shape coexistence
in neutron-deficient rare earth isotopes
Andreas Görgen
Service de Physique Nucléaire
CEA Saclay
Sunniva Siem
Department of Physics
University of Oslo
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Context
ultimate goal:
comprehensive microscopic description
of all nuclei and low-energy reactions
from the the basic interactions between
the constituent nucleons
ultimate goal:
comprehensive microscopic description
of all nuclei and low-energy reactions
from the the basic interactions between
the constituent nucleons
specific goal:
provide experimental data on nuclear
shapes and collectivity in a sensitive
region of shape transition and shape
coexistence for benchmarking
specific goal:
provide experimental data on nuclear
shapes and collectivity in a sensitive
region of shape transition and shape
coexistence for benchmarking
Inter-Nucleon
NN, NNN Interactions
AV18, EFT, Vlow-k
Theory of Light Nuclei
Verification: NCSM=GFMC=CC
Validation: nuclei with A≤16
Density Functional TheoryImproved functionals
remove computationally-imposed constraints
global properties of nuclei with A≥16
Dynamic Extensions of DFT
LACM, GCM, TDDFT, QRPA, CI, CC
Level densities
Low-energy Reactions
Hauser-Feshbach
Feshbach-Kerman-Koonin
Fissionmass and energy distributions
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Mean field and beyond: an example
Self-consistent HFB constrained to collective coordinate, e.g. (q20 ,q22)
set of basis states
potential energy surface qΦ
dqqf qii Φ=Ψ ∫ )(
Correlations beyond mean field
configuration mixing
properties of excited states: Ex, Qs, B(E2), … M. Bender et al.,
PRC 74, 024312 (2006)
Approaches / choices
collective coordinates: e.g. axial, triaxial, octupole, …
relativistic or non-relativistic
effective interaction: Skyrme, Gogny
Experiment: Ex, Qs, B(E2) from low-energy Coulomb excitation
Qs<0 Qs>0
experiment
E. Clément et al.,
PRC 75, 054313 (2007)
theory
prolate oblate γ vib.
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Multi-step Coulomb excitation
safe energy ⇒ purely electromagnetic excitation
transitional matrix element ⇒ B(E2)
diagonal matrix element ⇒ Qs reorientation effect ⇒ sensitive to nuclear shape
multi-step excitation
de-excitation γ-ray yields ⇒ dσσσσ/dθθθθ χ2 minimization of matrix elements to reproduce
experimental γ-ray yields
0+
6+
4+
2+0+
2+
4+
0+2+
[25°,54°] [54°,81°] [81°,115°] [115°,150°]
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3.3
2.5
2.0
1.0
E(4+) / E(2+)
148Dy
146Gd
144Sm
142Nd
140Ce
138Ba
136Xe
134Te
132Sn
150Er
146Dy
144Gd
142Sm
140Nd
138Ce
136Ba
134Xe
132Te
130Sn
148Er
144Dy
142Gd
140Sm
138Nd
136Ce
134Ba
132Xe
130Te
128Sn
142Dy
140Gd
138Sm
136Nd
134Ce
132Ba
130Xe
128Te
126Sn
140Dy
138Gd
136Sm
134Nd
132Ce
130Ba
128Xe
126Te
124Sn
134Sm
132Nd
130Ce
Region of interest
128Ba
126Xe
124Te
122Sn
828078767472
66
64
62
60
58
56
54
52
50
68
U(5)SU(3)2.0 3.33
E(5)
X(5)
Spherical
γ-softO(6)
2.2
2.5
2.9
3.3
Deformed
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Nuclear shapes
Oblate
Prolate
M. Girod,
CEA Bruyères-le-Châtel
Gogny HFB
G.A. Lalazissis et al. Nucl. Phys. A 597, 35 (1996)
RMF
region of
oblate shapes
rapid shape transition
shape coexistence ?
region of
oblate shapes
rapid shape transition
shape coexistence ?
oblate shapes in
medium / heavy nuclei
just beneath shell closure
holes in Ω=1/2 orbitals
oblate shapes in
medium / heavy nuclei
just beneath shell closure
holes in Ω=1/2 orbitals
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extensive studies at high spin
e.g. magnetic dipole bands
E.O. Lieder et al.
Eur. Phys. J. A 35, 135 (2008)
Previous experiments
no lifetimes known at low spin
only few non-yrast states from ββββ decay studies no experimental information on the shape at low spin
no lifetimes known at low spin
only few non-yrast states from ββββ decay studies no experimental information on the shape at low spin
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Predictions for 142Gd
configuration mixing calculation
GCM(GOA)
5-dimensional (q20,q22,α,β,γ)Gogny D1S interaction
parameter free
K=2
γ vib.
analytic solution of Bohr Hamiltonian
with square-well potential
E(5) symmetry
normalized to experimental Ex(2+)
and B(E2,2+→0+) from GCM(GOA)
oblate shape near ground state
transition to prolate at higher spin
γγγγ vibration built on oblate states
oblate shape near ground state
transition to prolate at higher spin
γγγγ vibration built on oblate states
experiment
need B(E2) values and
quadrupole moments
to test predictions
need B(E2) values and
quadrupole moments
to test predictions
M. Girod et al.
CEA Bruyères-le-Châtel
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Shape transitions
M. Girod et al.
CEA Bruyères-le-Châtel
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Shape coexistence ?
theoryexperiment
shape transitions
neutron number: spherical (N=82)⇒⇒⇒⇒ oblate (N=78) ⇒⇒⇒⇒ prolate (N<78)
proton number: prolate (Nd, Sm)⇒⇒⇒⇒ oblate (Gd, Dy)
spin: oblate near ground state (Gd)⇒⇒⇒⇒ prolate above 4+ (Gd)
shape transitions
neutron number: spherical (N=82)⇒⇒⇒⇒ oblate (N=78) ⇒⇒⇒⇒ prolate (N<78)
proton number: prolate (Nd, Sm)⇒⇒⇒⇒ oblate (Gd, Dy)
spin: oblate near ground state (Gd)⇒⇒⇒⇒ prolate above 4+ (Gd)
is there also shape coexistence ?
indication: low-lying 0+ states
(tentative) 0+ state in 140Sm at 990 keV
is there also shape coexistence ?
indication: low-lying 0+ states
(tentative) 0+ state in 140Sm at 990 keV
M. Girod et al.
CEA Bruyères-le-Châtel
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Simulation
142Gd + 208Pb
2.9 MeV / u
experimental level scheme
theoretical B(E2) and Qs
2×104 pps1 mg/cm2 208Pb
15 shifts
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Differential cross section
142Gd + 208Pb
2.9 MeV / u
experimental level scheme
theoretical B(E2) and Qs
[25°,54°] [54°,81°]
[81°,115°] [115°,150°]
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Sensitivity to quadrupole moments
experimental level scheme
theoretical B(E2) and Qs
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Proposed experiment
REX beams at maximum energy of 2.95 MeV / u
measured yields realistic beam intensities138Nd: ? (large) ~106
140Sm: 2×108 4×105142Gd: 1.2×106 2×104144Dy: ? ?
RILIS to suppress isobaric contaminants crucial
ionization schemes exist, Sm and Gd not yet tested at ISOLDE
Coulomb excitation target: 206Pb or 208Pb
(normalization point vs. spectrum simplicity)
double-sided annular silicon detector and MINIBALL
148Dy
146Gd
144Sm
142Nd
140Ce
138Ba
146Dy
144Gd
142Sm
140Nd
138Ce
136Ba
144Dy
142Gd
140Sm
138Nd
136Ce
134Ba
142Dy
140Gd
138Sm
136Nd
134Ce
132Ba
140Dy
138Gd
136Sm
134Nd
132Ce
130Ba
8280787674
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64
62
60
58
56
shape transition and coexistence predicted for N=78 isotones
measure quadrupole moments for 21+ (22
+, 41+) in 140Sm and 142Gd
measure transition rates between all low-lying states
identify low-lying 0+ states
extend study to 144Dy and N=76 if feasible
shape transition and coexistence predicted for N=78 isotones
measure quadrupole moments for 21+ (22
+, 41+) in 140Sm and 142Gd
measure transition rates between all low-lying states
identify low-lying 0+ states
extend study to 144Dy and N=76 if feasible
beam time request
140Sm: 6+3 shifts
142Gd: 15+3 shifts
testing required to determine / improve intensity and purity
beam time request
140Sm: 6+3 shifts
142Gd: 15+3 shifts
testing required to determine / improve intensity and purity
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Collaboration
CEA Saclay, IRFU/SPhN A. Görgen, W. Korten, A. Obertelli, B. Sulignano, Ch. Theisen
University of Oslo A. Bürger, M. Guttormsen, T.W. Hagen, P. Hoff, A.C. Larsen,
H.T. Nyhus, T. Renstrøm, S. Siem, H.K. Toft, G.M. Tveten, K. Wikan
CEA DIF, Bruyères-le-Châtel J.-P. Delaroche, M. Girod
CERN-ISOLDE J. Cederkäll, J. Van de Walle
GANIL E. Clément, G. de France, J. Ljungvall
University of Liverpool P.A. Butler, M. Scheck
University of York D.G. Jenkins
University of Manchester S. Freeman
Universität Köln P. Reiter, M. Seidlitz, A. Wendt